Non-Locality and Zero-Knowledge MIPs

TL;DR

This paper explores the role of non-locality in zero-knowledge multi-prover protocols, showing that certain protocols are secure against local and entangled provers but not against no-signalling strategies, highlighting the importance of non-locality.

Contribution

It introduces a framework to quantify the non-local advantage of simulators and demonstrates protocols that distinguish between different classes of provers based on non-locality.

Findings

Protocols sound against local provers

Protocols sound against entangled provers

Protocols not sound against no-signalling provers

Abstract

The foundation of zero-knowledge is the simulator: a weak machine capable of pretending to be a weak verifier talking with all-powerful provers. To achieve this, simulators need some kind of advantage such as the knowledge of a trapdoor. In existing zero-knowledge multi-prover protocols, this advantage is essentially signalling, something that the provers are explicitly forbidden to do. In most cases, this advantage is stronger than necessary as it is possible to define a sense in which simulators need much less to simulate. We define a framework in which we can quantify the simulators' non-local advantage and exhibit examples of zero-knowledge protocols that are sound against local or entangled provers but that are not sound against no-signalling provers precisely because the no-signalling simulation strategy can be adopted by malicious provers.